What's Wrong with Big Clock Moving at 0.1C?

[S.Vasojevic]

Big clock is coming towards us at 0.1C. Seconds pointing hand is, say, green. From time it moves from 0 to 1 sec it will emmit 6 x 10 e14 wave crests. We will receive same number of crests in 0.9 sec, so it will look to us like that seconds pointing hand is moving every 0.9 sec, and being a little bluer. Lorentz factor for 0.1 C is 1.005, so 1/1.005 is 0.995. So time would appear to contract for object coming towards us. I know that this goes against SR, and that something is wrong with this picture, but I can't tell what.

 

[Doc Al]

Big clock is coming towards us at 0.1C. Seconds pointing hand is, say, green. From time it moves from 0 to 1 sec it will emmit 6 x 10 e14 wave crests. We will receive same number of crests in 0.9 sec, so it will look to us like that seconds pointing hand is moving every 0.9 sec, and being a little bluer. Lorentz factor for 0.1 C is 1.005, so 1/1.005 is 0.995. So time would appear to contract for object coming towards us. I know that this goes against SR, and that something is wrong with this picture, but I can't tell what.

The reason it appears that time contracts (instead of dilates) is that the source is moving toward you and thus the crests are squashed together. Once you correct for that effect, you'll find the usual time dilation factor.

The time to see the same number of crests is 0.9045 seconds. To correct for the fact that the source moves towards you, multiply by c/(c-v) = 1/.9. You'll get: 0.9045*(1/.9) = 1.005, the usual Lorentz factor showing time dilation.

 

[ZikZak]

As Doc Al says, in Relativity an "observation" is what you get once the effects of light-travel time are accounted for. This includes the Doppler Effect. An "observation" is not what you see through a telescope; it's what you calculate happened where and when, given the light rays that reach you and working backwards to their points of emission.